BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

108 Vlad Marţian et al
that all the components are constant, whereas in reality all these characteristics
are dependent of the SOC, and the dicharge current. The circuit diagram can be
seen in the Fig. 2.
Fig. 2 – Thervein model.
2.3. Non linear Dynamic Model
A more realistic model has been created by extending the Thervein
model. This new model takes into account the nonlinearities in the components
of the Thervein model. As we said earlier the internal resistance of the battery
R+R 0 and the open circuit voltage E 0 are dependent on the SOC of the battery,
and also on the temperature T of the battery.
Since we are interested in how the temperature of the battery changes in
time we will use a modification of this later model, which can be seen in a
simplified version in Fig. 3.
In this model different form Thervein model we have included the
internal resistance in the overvoltage resistance, for simplification purpose, and
the internal resistance R and the open circuit voltage E 0 are dependent on some
function of SOC.
Fig. 3 – Non linear dynamic model.
3. Modeling Implementation
If we want to know how the current and the voltage in the battery are
modified in time we have to solve a system of equations that include first order
differential equations and also algebraic equations. Doing it by hand it takes a
long time, and if one of the parameter is changed we will have to do it again.